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1、1?!A?9.1?oA?9.1?oA?A?3R.?Q.f?:?u?5?O?,q?R-Q.fff?ggg?:duR.f?Q.f?N?N?,?m?3S3?X.A?LAC?IO?Z?k?(?5.1?!A?9.2 A?n9.2 A?n?,AAA?CCC?kn?,z?*?p?I?X=x11x12x1px21x22x2p.xn1xn2xnp3A?,?m?5,C?1IOz?n,XIOzC?,4?IOzC?.1?!A?9.2 A?n?C?N?Xe:(1)?kOU1?2o?x11x12x1pPpk=1x1k=X1x21x22x2pPpk=1x2k=X2.xn1xn2xnpPpk=1xnk=XnX1X2XpPnl
2、=1Ppk=1xlk=Xdef=T1?!A?9.2 A?n?C?N?Xe:(1)?kOU1?2o?x11x12x1pPpk=1x1k=X1x21x22x2pPpk=1x2k=X2.xn1xn2xnpPpk=1xnk=XnX1X2XpPnl=1Ppk=1xlk=Xdef=T1?!A?9.2 A?n(2)z?X?5?z?”V”?P,-P=1TXdef=(pij)np?pij=1Txij.?Jw?0 6 pij6 1,?nXi=1pXj=1pij=1.?pij?n)?xij?y?V,P?AAA?.1?!A?9.2 A?nrPL?L:p11p12p1pP1p21p22p2pP2.pn1pn2pnpPn
3、P1P2Pp1?Pj=nXi=1pij?n)?1j?C?V(j=1,p);Pi=pXj=1pij?n)?1i?C?V(i=1,n);1?!A?9.2 A?n(3)lA?P?uO?C?(R.f?),?rP?n?1?p?mn?:.1.?:?yV?K?,R0i=?pi1Pi,pi2Pi,pipPi?(i=1,n)?i?/?,p?C?31i?+(rowprofiles),1?!A?9.2 A?n(3)lA?P?uO?C?(R.f?),?rP?n?1?p?mn?:.1.?:?yV?K?,R0i=?pi1Pi,pi2Pi,pipPi?(i=1,n)?i?/?,p?C?31i?+(rowprofiles),
4、1?!A?9.2 A?n?C?j?K?,?1k?1l?m?l“(k?l):D2(k,l)=pXj=1?pkjPkpljPl?2,Pj=pXj=1 pkjPkpPjpljPlpPj!2.(1)1?!A?9.2 A?n2.?C?j?K?,r1i?:?Iz?pi1PiP1,pi2PiP2,pipPipPp!(i=1,n).3.1i?:?VPi?5O?1j?C?:nXi=1pijPipPj Pi=pPj(j=1,2,p)1?!A?9.2 A?n2.?C?j?K?,r1i?:?Iz?pi1PiP1,pi2PiP2,pipPipPp!(i=1,n).3.1i?:?VPi?5O?1j?C?:nXi=1pij
5、PipPj Pi=pPj(j=1,2,p)1?!A?9.2 A?n4.?O?1i?C?1j?C?aij=nX=1?piPPipPi?pjPpPjpPj!P=nX=1?piPPipPPi?pjpPPjpPPj!=nX=1pi PPiPPipj PPjpPPj=nX=1zizj(2)1?!A?9.2 A?n?zi=pi PPiPPi=xi XXi/TXXi-Z=(zij)?n p?,KC?m?SR=Z0Z=(aij)pp.1?!A?9.2 A?n(4)lA?P?uO?m?(Q.f?).aq?n?m?SQ?SQ=ZZ0=(bij)nn.(5)?1?AC?,-Z=(zij)np,?zij=pij Pi
6、PjpPiPj=xij XiXj/TpXiXj(i=1,n;j=1,p).(3)“(3)=?R.?Q.f?AC?“.1?!A?9.2 A?n(4)lA?P?uO?m?(Q.f?).aq?n?m?SQ?SQ=ZZ0=(bij)nn.(5)?1?AC?,-Z=(zij)np,?zij=pij PiPjpPiPj=xij XiXj/TpXiXj(i=1,n;j=1,p).(3)“(3)=?R.?Q.f?AC?“.1?!A?9.2 A?n(4)lA?P?uO?m?(Q.f?).aq?n?m?SQ?SQ=ZZ0=(bij)nn.(5)?1?AC?,-Z=(zij)np,?zij=pij PiPjpPiP
7、j=xij XiXj/TpXiXj(i=1,n;j=1,p).(3)“(3)=?R.?Q.f?AC?“.1?!A?9.2 A?nXJr?p?C?w?5?p?a8;?rn?w?5C?n?a8,?X?w?d*?“LOL.kdV?“LX?A?P:P=(pij),pij=1Txij(i=1,n;j=1,p).?n p,?rank(P)=p.dA?P5?AC?“:1?!A?9.2 A?n(1)P%z,-pij=pij PiPj=pij mij/T?mij=XiXjT=T PiPj,b1?5C?31(i,j)?“?.PP=(pij)np,P1p=0,rank(P)6 p 1.-Dr=diag(P1,Pn)
8、,Dc=diag(P1,Pn)(4)1?!A?9.2 A?n(1)P%z,-pij=pij PiPj=pij mij/T?mij=XiXjT=T PiPj,b1?5C?31(i,j)?“?.PP=(pij)np,P1p=0,rank(P)6 p 1.-Dr=diag(P1,Pn),Dc=diag(P1,Pn)(4)1?!A?9.2 A?n(2)PIOz?Z,-Z=D1/2rPD1/2c=(zij)np(5)?zij=pij PiPjpPiPj=xij XiXj/TpXiXj?AC?#?Z,?wdA?PL%z?IOz?1?!A?9.2 A?n(2)PIOz?Z,-Z=D1/2rPD1/2c=(z
9、ij)np(5)?zij=pij PiPjpPiPj=xij XiXj/TpXiXj?AC?#?Z,?wdA?PL%z?IOz?1?!A?9.2 A?n?uu?1?5C?2?O?2=nXi=1pXj=1(xij mij)2mij=nXi=1pXj=12ij(6)?2ijL1(i,j)?3u?1?5C?o2?O?z(cellchi2):2ij=(xij mij)2mij=Tz2ij?2=TnXi=1pXj=1z2ij=T tr(Z0Z)=T tr(SR)=T tr(SQ)1?!A?9.2 A?n?,AAA?nnn999?nnn9.2.1?SR=Z0Z,SQ=ZZ0,KSR?SQ?A?nnn9.2
10、.2evZ0Z?AuA?A?,Ku=ZvZZ0?AuA?A?.1?!A?9.2 A?n9.2.1(?)?Z?n p?,rank(Z)=m 6 min(n 1,p 1),Z0Z?A?1 2 m 0,-di=i(i=1,m),Kdi?Z?.XJ?3)“:Z=U V0,(7)?U?n n?V?p p?n p?(cm?d1,dm,?0),K)“Z=U V0?)1?!A?9.2 A?nPU=(U1U2),V=(V1V2),m=diag(d1,dm)?U1?n m?,V1?p m?,K?)“(7)?duZ=U1mV01(8)?nnn9.2.3?Z?A?)7?31?!A?9.2 A?n/?A?n,?lR.f
11、?u?Q.f?(J.duSR?SQk?A?,?A?qL?fJ?,dC?mRp?1?f,1?f,?1m?f,?mRnA?f3o?.lA?w,=Rp?:?Rp?f?l?,9RnC?:?Rn?A?f?l?.d?rC?:?:?N3?f(?(=?IX),?C?,?C?:?:?1a1?!A?9.2 A?nnnn,AAA?OOO?(1)d?X?uO?A?P?AC?#?Z(2)O?1?+?(1/?),PR=?xijXi?np=?pijPi?npdef=R01.R0nR?dX?(A?P)?z?1?1?,?8?3u?1:(=?:)?y”V”?K?.(3)O?+?(?/?),PC=?xijXj?np=?pijPj?
12、np=(C1,Cp).1?!A?9.2 A?nnnn,AAA?OOO?(1)d?X?uO?A?P?AC?#?Z(2)O?1?+?(1/?),PR=?xijXi?np=?pijPi?npdef=R01.R0nR?dX?(A?P)?z?1?1?,?8?3u?1:(=?:)?y”V”?K?.(3)O?+?(?/?),PC=?xijXj?np=?pijPj?np=(C1,Cp).1?!A?9.2 A?nnnn,AAA?OOO?(1)d?X?uO?A?P?AC?#?Z(2)O?1?+?(1/?),PR=?xijXi?np=?pijPi?npdef=R01.R0nR?dX?(A?P)?z?1?1?,?8?
13、3u?1:(=?:)?y”V”?K?.(3)O?+?(?/?),PC=?xijXj?np=?pijPj?np=(C1,Cp).1?!A?9.2 A?n(4)O?o.?2?O?,kd(9.2.3)?l“?,1k?1l?:?2?l?D2(k,l)=pXj=1?pkjPkpljPl?2/Pj=(Rk Rl)0D1c(Rk Rl).?rn?:(=1:)?%c?l?o?1/?:8N(R)?o.?Q:Q=nXi=1PiD2(i,c)=nXi=1PipXj=1?pijPi Pj?2=nXi=1pXj=1PiPj(pij PiPj)2P2i=nXi=1pXj=1(pij PiPj)2PiPj=nXi=1pXj
14、=1z2ij=2/T,(9)1?!A?9.2 A?n(4)O?o.?2?O?,kd(9.2.3)?l“?,1k?1l?:?2?l?D2(k,l)=pXj=1?pkjPkpljPl?2/Pj=(Rk Rl)0D1c(Rk Rl).?rn?:(=1:)?%c?l?o?1/?:8N(R)?o.?Q:Q=nXi=1PiD2(i,c)=nXi=1PipXj=1?pijPi Pj?2=nXi=1pXj=1PiPj(pij PiPj)2P2i=nXi=1pXj=1(pij PiPj)2PiPj=nXi=1pXj=1z2ij=2/T,(9)1?!A?9.2 A?n(5)IOz?#?Z?),Z=U1mV01,m
15、=rank(Z)6 min(n 1,p 1),?m=diag(d1,dm),V01V1=ImU01U1=Im3SAUO?z1+2+l1+2+l+m 0.80(0.70,0.85)(?f?l(l 6 m),1?!A?9.2 A?n(5)IOz?#?Z?),Z=U1mV01,m=rank(Z)6 min(n 1,p 1),?m=diag(d1,dm),V01V1=ImU01U1=Im3SAUO?z1+2+l1+2+l+m 0.80(0.70,0.85)(?f?l(l 6 m),1?!A?9.2 A?n(6)O?1?+?IG?+?IF.-ai=D1/2cvi,Ka0iDcai=1(i=1,m).R.
16、f?”f1?”(?+?I)?F=(d1a1,d2a2,dmam)=D12cV1m=d1P1v11d2P1v12dmP1v1md1P2v21d2P2v22dmP2v2m.d1Ppvp1d2Ppvp2dmPpvpm1?!A?9.2 A?n-bi=D1/2rui,Kb0iDrbi=1(i=1,m).Q.f?”f1?”(?+?I)?G=(d1b1,d2b2,dmbm)=D12rU1m=d1P1u11d2P1u12dmP1u1md1P2u21d2P2u22dmP2u2m.d1Pnun1d2Pnun2dmPnunm555:111?+?IIIG?+?IIIF?Q.?R.fff111?kkk?OOO.?111
17、?III?.G?ccc?LLL?111:(?:)?III,?F?ccc?LLL?111?(CCC?:)?III1?!A?9.2 A?n-bi=D1/2rui,Kb0iDrbi=1(i=1,m).Q.f?”f1?”(?+?I)?G=(d1b1,d2b2,dmbm)=D12rU1m=d1P1u11d2P1u12dmP1u1md1P2u21d2P2u22dmP2u2m.d1Pnun1d2Pnun2dmPnunm555:111?+?IIIG?+?IIIF?Q.?R.fff111?kkk?OOO.?111?III?.G?ccc?LLL?111:(?:)?III,?F?ccc?LLL?111?(CCC?:
18、)?III1?!A?9.2 A?n(7)3?1?+?IG?+?IF(?m=2)?:?.(8)o.?Q?2?O?)“.d(9)?(6)“?Q=nXi=1pXj=1z2ij=tr(Z0Z)=mXi=1i=mXi=1d2i(10)?i(i=1,m)Z0Z?A?,di=i(i=1,m)Z?.?A?2=TQ=TmXi=1d2i(11)(9)?:?C?:?1a,(?;?1)”1?!A?9.2 A?n(7)3?1?+?IG?+?IF(?m=2)?:?.(8)o.?Q?2?O?)“.d(9)?(6)“?Q=nXi=1pXj=1z2ij=tr(Z0Z)=mXi=1i=mXi=1d2i(10)?i(i=1,m)Z
19、0Z?A?,di=i(i=1,m)Z?.?A?2=TQ=TmXi=1d2i(11)(9)?:?C?:?1a,(?;?1)”1?!A?9.2 A?n(7)3?1?+?IG?+?IF(?m=2)?:?.(8)o.?Q?2?O?)“.d(9)?(6)“?Q=nXi=1pXj=1z2ij=tr(Z0Z)=mXi=1i=mXi=1d2i(10)?i(i=1,m)Z0Z?A?,di=i(i=1,m)Z?.?A?2=TQ=TmXi=1d2i(11)(9)?:?C?:?1a,(?;?1)”1?!A?9.3 Af9.3 Af9.3.1 L9.1?I31973c?1978cm?8I?N?1979A?T|?g?z191?!A?9.3 AfFigure:?1?!A?9.3 AfFigure:1?!A?9.3 AfFigure:1?!A?9.3 AfFigure:1?!A?9.3 Af9.3.2 A?I?|?7?C?A?|?B?X|?C?4|?D?9?|?E?|?F?G?W!F9?|?/=?k10?!S?!3?!?w!?9?!?H!oA!B!?!?L9.21?!A?9.3 Af1?!A?9.3 Af1?!A?9.3 Af